I am also having trouble with the latest version of Contact Form 7 (4.9.1) and an AJAX loading plugin.
I was able to solve my problem by moving the jQuery “on ready” function in scripts.js that calls wpcf7.initForm to after the initForm function is defined. I think the code works on the first load, when the DOM is still loading, but on an AJAX load when the DOM is already loaded, initForm gets called before it is defined.
I know this is a quirky case, but perhaps you could consider this change in a later version of the plugin.
Thanks.
The problem was that my categories were empty.
I created a dummy post and put it under each category and now the category templates display.